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Homework answers / question archive / Mrs Okoth invests a sum of money for her retirement which is expected to be in 20 years’ time
Mrs Okoth invests a sum of money for her retirement which is expected to be in 20 years’ time. The
money is invested in a zero coupon bond which provides a return of 8% per annum effective. At
retirement, she requires sufficient money to purchase an annuity certain of KES 1,200,000 per annum
for 25 years. The annuity will be paid monthly in arrear and the purchase price will be calculated at a
rate of interest of 6% per annum convertible half-yearly.
The annuity will be paid monthly in arrear and the purchase price will be calculated at a rate of interest of 6% per annum convertible half-yearly.
We need to calculate the monthly interest rate, r.
(1 + r)6 = 1 + 6% / 2 = 1.03
Hence, r = 1.031/6 - 1 = 0.4939%
Annuity per month, A = 1,200,000 / 12 = 100,000
PV of annuity at retirement = A/r x [1 - (1 + r)-n] = 100,000 / 0.4939% x [1 - (1 + 0.4939%)-12 x 25] = 15,629,722.53
Hence, the sum of money to be invested today = PV of the value above = 15,629,722.53 x (1 + R)-N
= 15,629,722.53 x (1 + 8%)-20
= KES 3,353,328.95
